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To unify this evaluation, we introduce $\\textit{Weighted Regret}$. Under this metric, we prove the $\\textit{Duality of Regret Conservation}$: purely deterministic procedures ensuring strict FDR control inevitably incur an $\\Omega(T)$ linear regret penalty, as threshold depletion during signal-sparse cold starts forces massive false negatives. Tailored for exogenous testing streams, we propose Decoupled-OMT (DOMT) as a baseline-agnostic meta-wrapper. By incorporating a history-decoupled, strictly non-negative random perturbation, DOMT rescues purely deterministic baselines from severe threshold depletion. 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By incorporating a history-decoupled, strictly non-negative random perturbation, DOMT rescues purely deterministic baselines from severe threshold depletion. 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